Safe Feedback Optimization through Control Barrier Functions

TL;DR

This paper introduces a feedback optimization method using high-order control barrier functions to ensure continuous state constraint enforcement while maintaining system stability and optimality.

Contribution

It proposes a novel control approach that guarantees safety constraints are always satisfied in feedback optimization, addressing a key open problem in the field.

Findings

Controller dynamics are well-posed and safe.

Equilibrium points correspond to optimization critical points.

Achieves local and global stability in convex cases.

Abstract

Feedback optimization refers to a class of methods that steer a control system to a steady state that solves an optimization problem. Despite tremendous progress on the topic, an important problem remains open: enforcing state constraints at all times. The difficulty in addressing it lies on mediating between the safety enforcement and the closed-loop stability, and ensuring the equivalence between closed-loop equilibria and the optimization problem's critical points. In this work, we present a feedback-optimization method that enforces state constraints at all times employing high-order control-barrier functions. We provide several results on the proposed controller dynamics, including well-posedness, safety guarantees, equivalence between equilibria and critical points, and local and global (in certain convex cases) asymptotic stability of optima. Various simulations illustrate our results.